It is also known that, to keep the system light and allow it to support the load being applied to the central hub of the wheels, the transmission of the efforts is born by spokes connecting the rim to the hub.
The spokes are suitably positioned according to two typical angles, the camber angle and the crossing angle. The first angle is that formed by each spoke in respect of the plane perpendicular to the wheel hub crossing the center line of the rim. This angle makes the system laterally stable to the right and to the left. The spokes depart from the center line of the rim and reach the hub, on the right and left flange thereof, at a suitable distance. They are positioned alternatively on the right and on the left.
The crossing angle is instead that which gives stability to the wheel in the torsional sense. If this angle were not provided for the spokes, the system would be unstable and any torsional stress, due to braking or acceleration, would cause a reciprocal rotation of the hub in respect of the rim, as the spoke--if positioned radially--would be unable to react to bending stresses, but would only react to tractive efforts or compressive stresses. For these reasons, and to keep the system stable, half of the right spokes and half of the left spokes are positioned in opposing directions.
Different executions are realized, according to the various types of performances having to be obtained, as far as lightness, air resistance, elasticity of radial comfort and so on.
Thus, the traditional wheels of sports bicycles can comprise 24-28-32-36 or 40 spokes.
Within the range of the variable "amount of spokes", there are furthermore hubs having differently spaced flanges, for a greater or smaller camber, and hubs whereon the holes for connection of the spokes are obtained along rims of different diameter, for a greater or smaller crossing angle.
In addition to this, to give a gradually higher torsional rigidity, the assembly can be done with a two, three or four crossing; this means that a spoke with dextrorotatory inclination meets two, three or four times--in its path from the hub to the rim--spokes having a left-handed inclination.
Within the range of all the variables heretofore described, it can be understood that the two camber and crossing angles differ from case to case.
In almost every case, the rims are constructed to face the problem of inclination of the spoke emerging from the rim only in the sense of the camber, while for the crossing angle the spoke's bearing on the rim is of the radial type.
A spoke for bicycle wheels is normally made with the end housed into the hub hole bent at 90.degree. to its axis, and riveted to prevent its outlet from said hole. The other end is threaded to be screwed into a bush or nipple, which is threaded inside and has a frustoconical head for bearing on the rim. The spokes thus easily take up the angular positioning imparted on them, while their correct tension is established by appropriate screwing of the nipple on its outer part.
It is clear that the nipple bears on the rim with a frustoconical surface and that, since the hole for housing the nipple is obtained by piercing the wall of the inner element of the rim, said frustoconical surface bears onto a round-shaped edge having a radial axis; the crossing angle is hence not accomplished.
The described geometrical arrangement repeats itself also when a strengthening eyelet is inserted into the hole housing the nipple, and even when a stiffening bush is added between the outer element housing the tubular tire and the inner element for connection of the nipple.
With this arrangement, when the nipple is positioned slanting in respect of the circle formed by the edge of the hole, there is a zone of contact between the nipple and the wheel rim which is limited, in theory, to three geometrical points, and when a pressure is imparted to put the spoke under tension, the surface of these three points widens through strain proportionally to the specific pressure and to the strain strength of the two materials forming the nipple and the eyelet.
Within the range of the shapes involved and of the differences between the diameter of the inner cylinder of the eyelet and the outer diameter of the cylindrical section of the nipple, said nipple is normally positioned inclined by a far narrower angle than that taken up by the spoke for its geometrical settlement.
One thus has a nipple which is apt to move axially towards the wheel center, when a variable pressure is imparted on its limited zone of contact, and a spoke emerging from the nipple which forms an angle between the axis of its threaded zone in engagement with the nipple and the direction which it takes up to reach the hole in the hub.
Either of these two defects cause a loosening of the spokes while running, and reduce the life thereof due to the constant bending in correspondence of the angle where they emerge from the nipple.
It should be noted that the pre-tension state of the spokes is at the basis of the geometric stability of the rim of bicycle wheels. Normally, a spoke is extended by a few millimeter tenths in the range of elastic strains, in order to provide stability to the general structure of the hub-spokes-rim system, and a one millimeter hundredth yielding of one of the pre-tension bearings slackens by about 5% the tension of the spoke.
Besides, the initial curve in the spoke conformation has in its zone emerging from the nipple--owing to the heretofore described lack of concentricity--a curvature depending on the flexural rigidity of said spoke; such a curvature is reduced by pulling actions on the running spoke (and each reduction of said curvature increases the distance available between the two hub-rim bearings, thereby reducing its tension).
In running conditions, the wheel bearing on the ground receives the load of the cyclists's weight and of the bicycle from the hub, reducing the tension of the four or five spokes positioned in the neighbourhood of the point contacting the road and causing them to work under compression.
For a bicycle running at 40 Km/h, the traction on said spokes is reduced, and returns to the initial extent of about 40%, when they leave the zone of contact with the road, with a frequency of 5-6 times per second.
The "hammering" deriving therefrom determines, on one hand, the widening of the zone of contact of the nipple on the eyelet and, on the other hand, a reduction in the initial curvature of the spoke emerging from the nipple. Both things cause an approach between the pre-tension bearings of the spoke, reducing its axial tension.
As the phenomenon is casual, in the neighbourhood of the equilibrium reached in the assembly stage, there are spokes which lose tension to a considerable extent and others which lose less tension.
This loosening difference at once causes a rim deformation, especially in respect of the plane in which it lies. (With a radially stiff rim, the 0.01 mm yielding in the bearings causes a side shifting of the rim by 2.4 mm).
Now, when a rim twists in its plane, the bicycle skids sideways, compelling the cyclist to be more careful and to reduce the speed.
On the other hand, the described alternative action, whereby the spoke curvature in its zone emerging from the nipple is first reduced and then again increased, subjecting said spoke to alternating bending stress, abbreviates the life of the spoke which would instead be practically endless if the same were to be subjected to pure alternating tensile stress. Considering these drawbacks deriving from the structural arrangement adopted at present for bicycle wheels, the ideal solution to the problem would be to cause the nipple to bear onto the whole circular surface of the eyelet already in the first assembly, so as to cover a wide bearing surface with low specific pressure and no longer deformable upon cyclic change of the contact pressure, and to supply the circle of the contact edge with an axis mating with the axis which the spoke has to take up in order to eliminate the angle being formed where emerging from the nipple.
An accurate study of all the assembly conditions has been able to establish that, starting from the hole for the tire valve, all the spokes always maintain a constant condition of the camber angle and of the crossing angle. Which means, for example, however operate the variables concerning the number of spokes and the number of crossing, the spoke n after the valve hole, always has--for instance--a right-handed camber and a left-handed crossing angle, or viceversa.
There are, namely, four fundamental arrangements:
On the right of the valve hole:
right-handed camber, left-handed crossing angle; PA1 left-handed camber, right-handed crossing angle; PA1 left-handed camber, right-handed crossing angle; PA1 right-handed camber, left-handed crossing angle.
On the left of the valve hole:
Furthermore, on varying of the crossing conditions, of the number of spokes, of the distance between flanges and hubs, and of the rim diameter along which are provided the holes for connection to the hub, for each spoke the variable of the two camber and crossing axes angles is reduced to a very small entity--such as to be easily absorbed by the deformations of the system during assembly--when using the precaution to position the nipple bearing seat with its axis on the bisecting line of the mean angle, between that of maximum deviation and that of minimum deviation of the spokes, depending on their variable assembly conditions, taking into account each possible combination.
The order of magnitude of the possible error is then reduced to 1/20 of the error actually existing on the usual production, practically undoing all the negative effects thereof.